A solid glass paperweight is a cone of volume $1232{\text{cm}}^3$ standing on a base of diameter 14 cm. Find its height in cm. Take π = 22/7.

The base diameter is 14 cm, so the radius is 7 cm. From (1/3)π$r^{2}h=1232,(1/3)(22/7)(49)h=(154/3)h=1232$, so $h=1232\times 3/154=24$ cm. (Reading 14 cm as the radius makes the base four times too wide and gives 6 cm; leaving out the 1/3 gives 1232/154 = 8 cm; using ½ in place of ⅓ gives 16 cm.)